Cubes & Cube Roots
What is the difference between a square root and a cube root?
Square roots opposites with x2
Cube roots opposites with x3
Evaluate the following expression
3sqrt255-13
32
Determine if the following statement is true sqrt97 is Rational.
False
Define the following:
Integer
Whole Number
Natural Number
Integer - All positive & negative counting numbers
Whole Number - Positive counting numbers starting with 0
Natural Numbers - Positive counting numbers starting with 0
List the following in order from greatest to least.
1.6^3
2sqrt3
sqrt11
63/17
root(3)27
root(3)27
sqrt11
2sqrt3
63/17
63/17
1.3^3
The value of root(3)k lies between 4.3 and 4.4. What are the possible values of k.
64
62
80.5
20
91
84
80.5
84
Give the two square roots of the following values:
15987
729
1331
789
+- 126.44
+-27
+-36.48
28.10
What is the difference between rational and irrational numbers?
Rational numbers can be written as both fractions and decimals that terminate or repeat
Irrational numbers cannot be written as fractions and are only decimals that are non-repeating & non-terminating
Why is the sqrt57 considered an irrational number?
Two Equations are shown, where a>0.
What is the value of b?
a^2 = 64
b^3 = a
b = 2
Give the decimal estimation of the value below and Between which two integers does the cube root below fall between:
-root(3)99
-4.626...
Between -5 and -4
Between which two integers does the square root below fall between
sqrt40
6 and 7
Classify the following numbers as either rational or irrational.
3.75
-16
1/9
sqrt135
6pi
root(3)18
2pi/7
3.75
-16
-7.98
Rational
3.75
-16
-7.98
1/9
Irrational
sqrt135
6pi
2pi/7
root(3)18
Complete the following statements with sometimes, always, or never.
Integers will ________ be whole numbers.
Natural numbers will _____________ be whole numbers.
Irrational numbers will ________________ be rational.
Integers will sometimes be whole numbers.
Natural numbers will always be whole numbers.
Irrational numbers will never be rational.
Convert the following Values to Fractions.
0.125
.8888888888...
.42
1/8
8/9
21/50
A cube has a volume of 1798 cubic inches. What is the length of one side of the cube?
12.16in
Approximate -sqrt2 to the nearest hundredth and determine which two integers it lies between.
-1.41
Between -2 & -1
Classifying the following decimals as terminating or non-terminating.
A. 0.12222222222....
B. 0.7878
C. 2/9
D. 0.123456
E. 9.6453
F. sqrt121
G. 0.56666666666
Terminating
B, D, E, F
Non-Terminating
G, C, A
Using the glues given and your knowledge of real numbers to determine which of the real numbers listed below could math.
- I am Rational
- I am not a Whole Number
- I am not a Natural Number
A. -19
B. 2
C. sqrt28
D. 1/3
E. -7.82
F. 7.35697...
A
E
Travis Kelce wants to build Taylor Swift a beautiful rose garden. He needs the garden to be 263 square feet. What is the approximate length of one side of the garden?
(round to the hundredths place)
16.22 ft2
If a number is Rational, does that is mean it is also an integer? Why or why not?
No because Integers cannot be decimals as they are only the positive and negative counting numbers on a number line. Rational numbers CAN have decimals or fractions.
An expression is given that has a value between 6 and 7 where x is a whole number.
What a possible value for x?
sqrt6 + sqrtx
x = 13 through 20
statement is shown.
"The square root of sqrt x is a number that is non-terminating and non-repeating."
Select all of the values of sqrt x that make the statement true.
A. x = 5
B. x = 9
C. x = 198
D. x = 25
E. x = 98
A, C, E
Classify the following real numbers:
5+ root(3)45
10sqrt12-15sqrt13
-sqrt36+5sqrt144
8.556... -> Real, Irrational
-19.44225... -> Real, Irrational
54 -> Real, Rational, Integer, Whole, Natural
Jenna Marbles is having a pool installed in her backyard and the contractor told her they need 25643 square feet of space for the pool/patio. What is the perimeter of pool/patio?
(round to the nearest hundredth)
640.54 ft2